Formative Assessment Lessons
- 827 Downloads
Formative assessment is the process by which teachers and students gather evidence of learning and then use this to adapt the way that they teach and learn in the classroom. In this paper, we describe a design-research project in which we integrated formative assessment into mathematics classroom materials. We outline two examples of formative assessment lessons, one concept-based and the other problem-solving, highlighting the important roles within them of pre-assessment, formative feedback questions, and sample work for students to critique.
KeywordsConceptual understanding Formative assessment Problem solving Mathematics task design Teacher professional development
We would like to thank our Shell Centre designer-researcher colleagues at the University of Nottingham, Nichola Clarke, Rita Crust, Clare Dawson, Sheila Evans and Marie Joubert, along with David Martin and Daniel Pead; the observer-researchers around the US, led by David Foster, Mary Bouck and Diane Schaefer; Alan Schoenfeld, Hugh Burkhardt and Phil Daro, who led the project; and the Bill and Melinda Gates Foundation for the funding that made possible this core contribution to their ‘College and Career Readiness’ strategy for Mathematics.
- Bereiter, C. (2002). Design research for sustained innovation. Cognitive Studies, Bulletin of the Japanese Cognitive Science Society, 9(3), 321–327.Google Scholar
- Black, P., Harrison, C., Lee, C., Marshall, B., & Wiliam, D. (2003). Assessment for learning: Putting it into practice. Buckingham, England: Open University Press.Google Scholar
- Black, P., & Wiliam, D. (1998). Inside the black box: Raising standards through classroom assessment. London, England: King’s College London, School of Education.Google Scholar
- Black, P., & Wiliam, D. (1999). Assessment for learning: Beyond the black box. Cambridge, England: University of Cambridge, Institute of Education.Google Scholar
- Burkhardt, H. (2006). From design research to large-scale impact: Engineering research in education. In J. van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen (Eds.), Educational design research (pp. 121–150). London, England: Routledge.Google Scholar
- Cusi, A., Morselli, F., & Sabena, C. (this volume). The use of digital technologies to enhance formative assessment processes. In D. R. Thompson, M. Burton, A. Cusi, & D. Wright (Eds.), Classroom assessment in mathematics: Perspectives from across the globe (pp. 77-92). Cham, Switzerland: Springer International Publishing AG.Google Scholar
- Evans, S., & Swan, M. (2014). Developing students’ strategies for problem solving in mathematics: The role of pre-designed “Sample Student Work”. Educational Designer, 2(7). Retrieved from http://www.educationaldesigner.org/ed/volume2/issue7/article25/.
- Hatano, G., & Inagaki, K. (1986). Two courses of expertise. In H. W. Stevenson, H. Azuma, & K. Hakuta (Eds.), Child development and education in Japan (pp. 262–272). New York, NY: W. H. Freeman/Times Books/Henry Holt & Co.Google Scholar
- Herman, J., Epstein, S., Leon, S., La Torre Matrundola, D., Reber, S., & Choi, K. (2015). Implementation and effects of LDC and MDC in Kentucky districts. CRESST Policy Brief No. 13. Retrieved from http://www.cse.ucla.edu/products/policy/PB_13.pdf.
- IR [Inverness Research]. (2015). Mathematics assessment program (MAP): Project Portfolio. Retrieved from http://inverness-research.org/mars_map/xindex.html.
- Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.Google Scholar
- Schoenfeld, A. H. (1985). Mathematical problem solving. London, England: Academic Press.Google Scholar
- Sierpinska, A. (1994). Understanding in mathematics. London, England: Falmer.Google Scholar
- Swan, M. (2015). Designing formative assessment lessons for concept development and problem solving. In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez, (Eds.), Proceedings of the 37th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 33–51), November 5–8, 2015. East Lansing, Michigan, USA.Google Scholar
- Swan, M., & Burkhardt, H. (2014). Lesson design for formative assessment. Educational Designer, 2(7). Retrieved from http://www.educationaldesigner.org/ed/volume2/issue7/article24.
- van den Akker, J., Gravemeijer, K., McKenney, S., & Nieveen, N. (Eds.). (2006). Educational design research. London, England and New York, NY: Routledge.Google Scholar
- Wiliam, D., & Thompson, M. (2007). Integrating assessment with instruction: What will it take to make it work? In C. A. Dwyer (Ed.), The future of assessment: Shaping teaching and learning (pp. 53–82). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Wright, D., Clark, J., & Tiplady, L. (this volume). Designing for formative assessment: A toolkit for teachers. In D. R. Thompson, M. Burton, A. Cusi, & D. Wright (Eds.), Classroom assessment in mathematics: Perspectives from across the globe (pp. 207-228). Cham, Switzerland: Springer International Publishing AG.Google Scholar